Guards and Templars are perfect names. But I'm not sure about Praetorians. They were essentially improved legionaries or the emperor's personal bodyguards. Therefore, their connection to the order seems questionable.
Added 2 minutes later
Although I can't think of more suitable names right now.
As for the order, I'll say this - if it wasn't in the sixth game, then after the change of regime, it could have been an order based on old codes and oaths.